ユーザー:Dkwingsmt/How stats grow
This article discusses how stats (HP/ATK/DEF) grow with levels. It is derived from the collected data shown in this spreadsheet. Thanks to a few people who contributed data. Feel free to make a clone of this spreadsheet for you own research! Stats grow approximately in linear The first thing we can notice is Stats grow in a linear fashion against level, which is N(L) = k L + N(1) where N is any of HP, ATK or DEF, N(L) is the stat at level L , and k is an coefficient from linear fitting. This formula can predict actual data with an error up to 0.7%. But there is more to know to derive the actual formula. Spurting The most mysterious behavior of the growth curve is how the stats "spurts", i.e. non-regular burst of growth at certain level. For example, Oriko 3\* usually grows around 147/62/47 per level, but occasionally (once every about 15 levels) it becomes 185/78/59. Masara 4* usually grows 140/63/44, but sometimes it's 186/84/60 and it happens more often (once every 3/4 levels). Some clues to this are: # Characters of the same rarity spurts at the same levels, and with almost the same proportion. # The proportion of spurted growth to the unspurted ones is a constant, and it is close to a simple fraction, which is 4/3 for 4*, and 5/4 for 3* and 2*. We make the following guess: There is a "Spurting Level" L_s . It is a rounded integer that grows linearly against the level L with a non-integral coefficient "Spurting coefficient" k_s , L_s(L) = \lfloor k_s (L-1)\rfloor Stats grow linearly to the spurting level with another "growing coefficient" k_N , N(L) = \lfloor k_N L_s + N(1)\rfloor Since the coefficient is non-integral, the fraction part of L_s accumulates as level grows, and when it accumulates over 1, the spurting level grows 1 more than usual, which forms a "spurt". Apply the spurting model We managed to apply the spurting model above to the stat tables, which are recorded at column I to column P of each table. We first tried to guess the spurting coefficient. It should be between 3 and 4 for 4*, and between 4 and 5 for 3* and 2*. And by manual adjusting, we can find such numbers that predicts spurting levels as the recorded data, which are And based on that, we find the coefficients of stats against L_s , resulting in column K-M. Column N-P show how this formula performs - the absolute error is no more than 1. What's more surprising is that all three of $k_N$s of Orico 3* is exactly 1/100.00 of her level 1 stats. This makes us believe that, although the spurting coefficients look arbitrary, this model should be correct. (For other girls, this proportion is not always 1/100.00, but between 1/103 to 1/97). Derive the spurting coefficient We try to find patterns from the relationship between the Lv1 stat and LvMax stat of each girl, which is recorded in table Max stats. We define the "maximum growth" of a stat to be percentage of the increased part of a stat at LvMax against the Lv1 stat, G = \frac{ N\left( L^\textrm{max} \right) - N(1) }{ N(1) } * 100 We multiply it by 100 for the convenience of later calculation. The table shows that, a character usually have similar G between the 3 stats, and that G of characters with the same rarity are also close. We use the G of the characters that have the same one between 3 stats, such as Orico 3*, resulting in It basically means that, when a 2* character grows to LvMax, all three of her stats are increased by roughly 220% times of her Lv1 stats. Aaaaaand here comes the miracle: I think we found the formula to derive the spurting coefficient. Derive the growing coefficient The Lv1 and LvMax stats are part of the basic properties of a character. We can derive the growing coefficients from them, now that we have the accurate formula of spurting. Unsolved problems The predicted values from this formula deviate from the true data by 1 or -1 occasionally. I have no clue how to solve it for now. Additionally, due to the lack of data, I don't know the benchmark G for 5* characters yet.